Robust optimization model for uncertain multiobjective linear programs

Lei Wang,Min Fang

doi:10.1186/s13660-018-1612-3

Abstract

In this paper, we consider the multiobjective linear programs where coefficients in the objective function belong to uncertainty sets. We introduce the concept of robust efficient solutions to uncertain multiobjective linear programming problems. By using two scalarization methods, the weighted sum method and the ϵ-constraint method, we obtain that the robust efficient solutions for uncertain multiobjective linear programs with ellipsoidal uncertainty sets and general norm uncertainty sets can be computed by some deterministic optimization problems.

Highlights

The parameter values of optimization problems in real world are usually uncertain due to prediction errors, estimation errors, or lack of information at the time of decision
We introduce the concept of robust efficient solution to uncertain multiobjective linear programs (UMLPs)
We show that two scalarization methods, the weighted sum method and the -constraint method, can be used to find robust efficient solutions of UMLP with ellipsoidal uncertainty sets and general norm uncertainty sets

Summary

Introduction

The parameter values of optimization problems in real world are usually uncertain due to prediction errors, estimation errors, or lack of information at the time of decision. Jeyakumar, Li, and Perez [21] introduced the definition of radius of robust feasibility and analyzed the robust weakly efficient solution of a multiobjective linear programming problems with data uncertainty both in the objective function and constraints. They gave numerically tractable optimality conditions for highly robust weakly efficient solutions. We further show that robust efficient solutions for uncertain multiobjective linear programming problems with ellipsoidal uncertainty sets and general uncertainty sets can be found by solving deterministic optimization problems using weighted sum scalarization and can be computed by existing technology of deterministic optimization problems

Ellipsoidal uncertainty sets Consider the ellipsoidal uncertainty sets l

General norm uncertainty sets Consider the general norm uncertainty sets

Conclusions